A Dual‐Kinetic Control Strategy for Designing Nano‐Metamaterials: Novel Class of Metamaterials with Both Characteristic and Whole Sizes of Nanoscale

Abstract Increasingly intricate in their multilevel multiscale microarchitecture, metamaterials with unique physical properties are challenging the inherent constraints of natural materials. Their applicability in the nanomedicine field still suffers because nanomedicine requires a maximum size of tens to hundreds of nanometers; however, this size scale has not been achieved in metamaterials. Therefore, “nano‐metamaterials,” a novel class of metamaterials, are introduced, which are rationally designed materials with multilevel microarchitectures and both characteristic sizes and whole sizes at the nanoscale, investing in themselves remarkably unique and significantly enhanced material properties as compared with conventional nanomaterials. Microarchitectural regulation through conventional thermodynamic strategy is limited since the thermodynamic process relies on the frequency‐dependent effective temperature, T eff (ω), which limits the architectural regulation freedom degree. Here, a novel dual‐kinetic control strategy is designed to fabricate nano‐metamaterials by freezing a high‐free energy state in a T eff (ω)‐constant system, where two independent dynamic processes, non‐solvent induced block copolymer (BCP) self‐assembly and osmotically driven self‐emulsification, are regulated simultaneously. Fe3+‐“onion‐like core@porous corona” (Fe3+‐OCPCs) nanoparticles (the products) have not only architectural complexity, porous corona and an onion‐like core but also compositional complexity, Fe3+ chelating BCP assemblies. Furthermore, by using Fe3+‐OCPCs as a model material, a microstructure‐biological performance relationship is manifested in nano‐metamaterials.

solvent of DMF and CH 2 Cl 2 (volume ratio of 1:10) containing PEO-b-P2VP (0.01 mg) and FeCl 3 ·6H 2 O with a varying molar ratio of vinyl pyridine/Fe 3+ of 60, 40, and 20 were prepared by stirring for at least 2 h to give a homogeneous solution. Subsequently, 4 μM of NaOH was added to the copolymer solutions, and then the mixture was stirred overnight to reach equilibrium. The prepared mixture solution was used as dispersed phase. The continuous phase was an aqueous solution of PVA with a concentration of 0.4 wt%. The two phases were pumped to the microfluidic device by a syringe pump (Harvard PHD 2000 Series); and in the sequential coflow regime, as shown in Figure 1a in the main text, the dispersed phase broke into highly monodisperse emulsion droplets because of interfacial tension. The droplet diameters could be readily tuned from 15 to 80 µm by the size of the orifice and the flow rates of the two phases. Immediately after formation, the micron-sized monodispersed droplets were sequentially extruded through a filter membrane with a size of 0.45 µm. The nano-sized droplets prepared through the second filter stage were too small to be studied in suit during the solidification process. Instead, we monitored the structural evolution of micron-sized droplets as indirect evidence to study the structural and morphological evolution of the nanosized droplets during the solvent evaporation. Although they were different in the dimensional sizes, both droplets were in non-equilibrium, and could be metastable with the droplets retaining their stability for extended periods of experimental time, because their interfaces were stabilized by a PVA surfactant. [1] The micron-sized droplets through first microfluidic stage were collected in a homemade container at room temperature. The structural and morphological evolution of the prepared droplets were carefully observed during the solvent evaporation. Depending on the geometry and the quantity of droplets, the evaporation of solvent took tens of minutes to hours, and we observed that the nano-sized droplets solidified faster just within 1 minute. Finally, after the impurities were removed by dialysis purification, Fe 3+ -OCPCs nanoparticle solution was obtained and placed at 4 ℃ for standby.

Characterization
Real time structural evolution of the emulsion droplets containing Fe 3+ /PEO-b-P2VP was monitored using Olympus IX71 inverted optical microscope in the bright-filed mode. The resulting hierarchical Fe 3+ -OCPCs structures were observed by transmission electron microscopy (TEM) images (HD-2000, Hitachi Ltd., Japan), operating at an acceleration voltage of 60 kV. Typically, Fe 3+ -OCPCs were welded into a frozen paraffin before cut into slices with a certain thickness using a Bühler high-speed diamond-blade saw equipped with water cooling, carefully transferred onto a copper TEM grid with a carbon supporting film and allowed to dry in air and at room temperature for 1 day. The P2VP domains which were chelated by Fe 3+ appeared dark in the TEM observations due to the high atomic number of Fe. I 2 vapor was employed to observe the phase separation structures in Fe 3+ 0 -OCPCs block copolymer nanoparticles because they could selectively react with the P2VP domains in Fe 3+ 0 -OCPCs. The suspensions of Fe 3+ 0 -OCPCs particles (0.5 mL) were stained with I 2 vapor for 2 h at room temperature. After staining, the stained particles were centrifuged (12000 rpm., 5 ℃, 15 min) and washed with deionized water to eliminate excess I 2 . After washing, the stained particles were redispersed in pure water with ultrasonication. Suspensions of the stained particles in water were dropped onto a carbon membrane surface placed on a Cu mesh and dried at room temperature. The phase separation structures in the particles were then observed by scanning transmission electron microscopy (STEM; HD-2000, Hitachi Ltd., Japan).The morphologies of Fe 3+ -OCPCs were observed by scanning electron microscopy (SEM) which was carried out on a FEI NOVA Nano400 instrument at an accelerating voltage of 60 kV. To prepare sample for SEM, the Fe 3+ -OCPCs on the glass substrates were coated with a thin layer of gold. Dynamic light-scattering measurements were carried out using Zetasizer, Malvern company, UK. equipped with a He-Ne Laser (632.8nm) for measuring the hydrodynamic size of the resultant Fe 3+ -OCPCs. Small-angle X-ray scattering (SAXS) measurements were performed on a Nanostar U small-angle X-ray scattering system using CuKa radiation (λCuKα= 1.5418 Å). The SAXS data at room temperature were collected over a 2θscattering range 0.5 -2.8°with a step 0.02. The magnetic properties were measured using vibrating sample magnetometer (VSM) and superconducting quantum interference device (SQUID). VSM data were collected on the BKY-400 magnetometer with a sensitivity of 2×10 -5 emu. SQUID magnetometry was performed using a Quantum Design MPMS with dc detection from Oxford Instruments. The pore size distribution profile of Fe 3+ -OCPCs was measured by nitrogen sorption at 77.3 K using a Micromeritics ASAP 24204 volumetric adsorption analyzer. Fe 3+ -OCPCs were degassed offline at 393 K for 12 h under dynamic vacuum  bar) before analysis, followed by degassing on the analysis port under vacuum, also at 393 K.
An inductively coupled plasma mass spectrometry (ICP-MS) Thermo iCAP RQ was used to measure the Fe and N content of the samples. The samples were digested by using HCl/HNO 3 (3/1 v/v). Fourier transform infrared (FTIR) spectra were obtained at room temperature using a Bruker EQUINOX 55 FTIR spectrometer.

Determined Fe 3+ concentration
Whether the biological experiments or subsequent T 1 -weighted MR image tests, we needed to determine accurately the Fe 3+ concentration in Fe 3+ -OCPCs and Fe 3+ -P2VP nanoparticles. The Fe 3+ concentration of the investigated solutions of the Fe 3+ -OCPCs and Fe 3+ -P2VP was determined by the procedure phenanthroline spectrophotometry. There were two principles of this method: first, according to Lambert Beer law: A = ε bC, A was the absorbance of a colored substance, and C was the concentration of the substance. When the incident light ε and the optical path b was constant, we could see that A was directly proportional to C.
Second, phenanthroline (phen) could form a stable orange red complex with iron ions within a certain pH range. The reaction equation was as follows: Fe 2+ + 3(phen) =Fe(phen) 3 2+ .
Therefore, this method needed to draw a standard curve first, then tested Fe 2+ according to the standard curve.
We first prepared iron standard solution. A small amount of deionized water was added to 0.484 mg FeCl 3 · 6H 2 O to dissolve it completely. After full dissolution, drained it with a glass rod and transferred the mixture to a 1000 mL volumetric flask, and finally diluted the mixture to the scale with an appropriate volume of deionized water. Then, we prepared 0.15% phenanthroline aqueous solution. 5-10 mL of 95% ethanol solution was added to 1.5 g phenanthroline. After full dissolution, drained the mixture with a glass rod and transferred it to a 1000 ml volumetric flask, and finally diluted the mixture to the scale with an appropriate volume of deionized water.
With all the prework completed, 1 mL hydroxylamine hydrochloride solution was added into iron standard solution (0 ml, 2 ml, 4 ml, 6 ml, 8 ml, 10 ml, 12 ml and 14 ml of 10 ml).Then, 2 mL 0.15% phenanthroline solution was added into the mixture, which appeared a colorless and transparent solution. After 10 minutes, 5 mL HAC NaAc buffer solution (pH = 4.6) was added into the prepared solution, shook well and stood for 10min. At this time, the liquid appeared transparent orange. Finally, drained the colorful mixture with a glass rod, and diluted to the 50 mL with deionized water. During the UV-Vis spectrum test, set the wavelength range between 350-700nm, and measured the UV-Vis spectrum of each solution.
Taking the absorption value of UV-Vis spectrum at 510 nm, the standard curve of iron concentration and correlation coefficient were obtained.

Light microscopy
To examine the structural and morphological evolution of the prepared droplets during the solidification process, phase contrast images of static bright field droplets were captured at different points of time, using the Olympus IX71 inverted optical microscope equipped with 60x phase-contrast objective. All image data shown were representative samples from three random fields.

Cell culture
HeLa cells were obtained from Yan group (Life Sciences Institute, Zhejiang University, Hangzhou). HeLa cells were maintained in DMEM supplemented with 10% FBS, penicillin (100 U/ml) and streptomycin (100 mg/ml) at 37 ℃ with 5% CO 2 . HeLa Cells were passaged every 48 h and split 1/2. For experiments, cells were incubated with fresh medium for 24 h to allow cell adhesion. Then the culture medium was replaced by fresh medium containing the nanoparticles, after which the experiments were carried out. The prepared anoparticles were sterilized prior to the addition to the culture medium by filtration with a sterile membrane filter of 0.65 µm pore diameter.

Cytotoxicity.
For the determination of cellular viability, HeLa cells seeded in 96-well plates at 5 × 10 4 cells per well and and cultured in 1640 culture medium overnight. Then, the culture medium was replaced by fresh medium containing a series of concentrations of Fe 3+ 0.06 -OCPCs (the Fe 3+ concentration is 0, 2, 10, 20 μM), Fe 3+ 0.06 -P2VP and Fe 3+ 0.02 -OCPCs as the control group.
After another 30 min of treatment, the supernatant containing the excrescent nanoparticles was decanted, and the residual nanoparticles were washed by the fresh media and the proportion of living cells was evaluated by CCK-8 assay. 10 μL CCK-8 was added to each well, followed by 2.5 h incubation at 37 °C. After this period, the OD value of each well was read out using a Microplate Reader (Microplate Titre Infinite F200, TECAN Spectra) at 450 nm. At each concentration, three individual experiments were carried out.         We firstly evaluated the biostability of Fe 3+ -OCPCs to ensure the in vivo applications. The filtrate of fibroblast cell culture medium was used to mimic cell microenvironment in normal tissues. We mixed Fe 3+ -OCPCs with the filtrate of cell culture medium in a cone-shaped tube.

Biostability in Cell Culture Medium
After t=0 (a), 6 (b), 12 (c), 24 (d), 36 (e), 48 (f) h immersion of the nano-metamaterials, the T 1 -weighted MR imaging of the filtrate was tested. As shown in Figure S8, we found that the MR imaging exhibited no obvious decrease after 36 h co-culturing, indicating that our Fe 3+ -OCPCs were biostable in culture medium.  where  I is the gyromagnetic constant for protons ( I =2.67510 +8 T -1 s -1 ); g is the electronic gfactor (g=2); S is the total electron spin of the Fe 3+ ion (S= 5/2 for Fe 3+ );  B is the Bohr magneton ( B = 9.27410 -24 JT -1 );  O is the permeability of vacuum ( O =1.25710 -6 NA -2 ); r FeH is the distance between the proton and the Fe 3+ ;  s and  I are the angular electronic and proton Larmor frequencies ( s =658 I and  I = I B where B is the magnetic field), A is the hyperfine coupling constant (in J) and  is the reduced Planck constant (  =h/(2)=1.05410 -34 Js). [3] In equation SI-5, the two terms inside the square bracket (the "3 term" and the "7 term") have field dependence. The "3 term" is a function of the nuclear precession frequency while the "7 term" is a function of the electron precession frequency. Since the magnetogyric ratio is much larger for an electron than for a proton (γ s /γ H ) =658, ω s 2 τ c2 2 will become much greater than 1 at a much lower magnetic field than ω I 2 τ c2 2 . At the field where ω s 2 τ c2 2 becomes greater than 1, the "7 term" disperses away to approach zero which has been proved in previous research. [3] Additionally, because of the ionic nature of bonding in Fe 3+ compounds (Fe 3+ -OCPCs), and the fact that the water proton is separated from the Fe 3+ ion by two bonds, the hyperfine coupling constant, A/p, is quite small. Thus the scalar mechanism in equation SI-5 is not very efficient; furthermore because of its 1/ω s2 dependence it has dispersed at frequencies below 10 MHz. As a result, the characteristic time T 1m can be expressed through equation 9 shown in the main text.
The correlation times  c1 ,  c2 and  e in equation SI-1 and SI-5 are defined as The time  R is the tumbling time of the complex and it can be estimated with the classical formula for spherical nanoparticles /2equal to about 10 and 130 MHz (for B=1.5T, I 65 MHz). [3] The outer-sphere contribution to the longitudinal relaxivity r 1 OS is given as and D is the sum of the diffusion coefficients of bulk water and of Fe 3+ -OCPCs; b FeH is the distance of closest approach of the water molecules to Fe 3+ in Fe 3+ -OCPCs. It has recently been shown that the outer-sphere contribution can be neglected compared to the inner sphere contribution for sufficiently large fields (B>0.25T) and for slow tumbling construct which are generally associated with large inner-sphere relaxivities. Under these conditions the ratio r 1 OS /r 1 IS is generally smaller than 0.1. However, for paramagnetic complexes such as Fe 3+ -OCPCs in our paper with small inner-sphere relaxivities, r 1 OS /r 1 IS could be close to unity. [3]

Discussion for the longitudinal relaxivity based on micromagnetic simulation and molecular rotational dynamics
The micromagnetic simulation and rotational dynamics analysis of paramagnetic Fe 3+ ions were conducted to further reveal the mechanism of the T 1 contrast enhancement of Fe 3+ -OCPCs. To simplify theoretical simulation and analysis process, we only considered the multilayered onion-like substructure of Fe 3+ -OCPCs. As shown in Figure S10, compared to homogeneous Fe 3+ -P2VP nanoparticles, the confinement of Fe 3+ ions in the hierarchical microarchitecture of Fe 3+ -OCPCs increases the local density of Fe 3+ ions. Thus, the local density of Fe 3+ in Fe 3+ -OCPCs is larger than that in Fe 3+ -P2VP. The increase in Fe 3+ local density can shorten the distance between neighbor Fe 3+ ions, further increasing magnetic dipolar interaction. Figure S10. The schematic illustration of the density differences between Fe 3+ -P2VP and the Fe 3+ -OCPCs. The yellow part represents Fe 3+ -P2VP domain while the blue part represents PEO domain. α represents the volume fraction of Fe 3+ -P2VP layers in Fe 3+ -OCPCs, which meets 0<α<1, making ρ 2 larger than ρ 1 .
By modeling the Fe 3+ ion as a paramagnetic sphere, we conducted the micromagnetic simulation and rotational dynamics analysis of paramagnetic Fe 3+ ions. Here, we selected two extreme circumstances to simulate the influence of the average distance between neighbor Fe 3+ ions. For the first circumstance where the distance between two paramagnetic Fe 3+ ions was long enough (corresponding to Fe 3+ -P2VP), we considered a 1×1 paramagnetic Fe 3+ sphere arrangement, denoted as (Fe 3+ ) i . For the second circumstance where the distance between two Fe 3+ ions was extremely short (corresponding to Fe 3+ -OCPCs), we considered a 1×2 paramagnetic Fe 3+ spheres arrangement, denoted as (Fe 3+ ) i and (Fe 3+ ) j . The orientations of the overall magnetic spin structures of the paramagnetic Fe 3+ spheres were visualized by using object oriented micromagnetic framework program (OOMMF, NIST). The principal calculation used in OOMMF simulation was based on the Landau-Lifshitz-Gilbert (LLG) equation. [4] The simulation results were obtained using the "Oxs_Uniform Exchange-Field" code. Based on the simulation results, we found that when two paramagnetic Fe 3+ ions are approaching each other in a certain magnetic field, the non-deviated spins (white arrows) in the right edges of (Fe 3+ ) i increased, indicating a stronger dipolar interaction between adjacent paramagnetic Fe 3+ ions ( Figure S11). Moreover, we also used the "Oxs_MinDriver-Spin" code to obtain more detailed and direct information of the spin structures of (Fe 3+ ) i and (Fe 3+ ) j by controlling minimization evolvers of internal spins ( Figure S12). The black arrows in the middle of Figure S12 become thicker, also indicating the stronger magnetic dipolar interaction.  Both "Oxs Uniform Exchange-Field code" and "Oxs_MinDriver-Spin" results indicate that the magnetic dipolar interaction is increased by shortening the distance between neighbor paramagnetic Fe 3+ ions. Notably, the increased interaction between paramagnetic Fe 3+ ions leads to a higher local viscosity around a Fe 3+ ion. [5] Consequently, compared to homogeneous Fe 3+ -P2VP nanoparticles, the confinement of Fe 3+ ions in the hierarchical microarchitecture of Fe 3+ -OCPCs increases the magnetic dipolar interaction and local viscosity of paramagnetic Fe 3+ ions.
The T 1 relaxation times of water protons induced by a single Fe 3+ electronic spin can be described as: [6]  where T 1, bulk is the relaxation time of Fe 3+ in Fe 3+ -OCPCs and ω 0 is the energy level splitting between the |m s = 0⟩ and |m s = ± 1⟩ states at zero external magnetic field. For each paramagnetic Fe 3+ ion i, γ i is the gyromagnetic ratio; B 2 ⊥,i is the rms transverse magnetic noise strength induced by neighbor Fe 3+ ; and τ c,i = 1/R i is the noise correlation time of neighbor Fe 3+ , the inverse of the noise fluctuation rate (R i ) [7] Since the rotational motion rates of paramagnetic Fe 3+ ions are typically in GHz range, the value of R i would be larger than ω 0 When the fluctuation rate of the neighbor paramagnetic Fe 3+ paramagnetic ion is larger than the resonant frequency of the Fe 3+ spin (R i > ω 0 ), a further increase in fluctuation rate results in a smaller noise spectrum intensity at the spin resonance frequency, further leading to a longer T 1 relaxation time of the water protons. The higher local viscosity induced by increasing dipolar interaction between neighbor paramagnetic Fe 3+ ions can decrease R i , further increasing r 1 relaxivity. Consequently, the increase in the local viscosity for Fe 3+ -OCPCs lead to the enhancement of magnetic dipolar interaction between neighbor paramagnetic Fe 3+ ions, thus resulting in the decreased R i value and the improved T 1 contrast effect. The Demonstration of the novelty of the concept "nano-metamaterials" nanomaterials have been widely applied in biological field. Nevertheless, there are no reports on the application of artificially structured nano-metamaterials with multilevel ordered microarchitectures in biomedical field. We searched on Web of Science Core Collection with key word 'nano-metamaterials' for related publications. Only 18 reports (except for 3 reviews and 1 journal article) popped up using the concept of nano-metamaterials (https://www.webofscience.com/wos/alldb/summary/591c5407-baef-4508-a626-96085f5444f0-3047f97a/relevance/1). In this field, the "ferroelectric nano-metamaterials" was an important research topic, accounting for almost 39% of the publications. For example, the concept of ferroelectric nano-metamaterials was firstly proposed and published on Scientific Reports. [11] The concept of nano-metamaterials was further applied in sensing such as Terahertz sensing [12] or shielding, [13] with a publication share of 33%. Other optical applications were also involved, such as photonic devices [14] and solar absorber. [15] These results indicated that the nano-metamaterials, as a branch concept of metamaterials, have not gained strong attention and were mainly applied for physics applications. Despite the concept of nano-metamaterials has been mentioned in different researches concerning ferroelectric materials and optical materials, we summarized that the researches in the past decades have three characteristics: (i) Numerical studies and computational analyses have been the mainstream while the synthesis protocols have not been widely discussed; (ii) Those nanometamaterials were always a two-dimensional (2D) nano-specimens consisting of numerous ordered building blocks, whereas the well-defined definition of nano-metamaterials has not been summarized and given, especially considering the microstructure of nano-metamaterials would further evolve from 2D microarchitecture to 3D microarchitecture; (iii) The applications of nano-metamaterials evolved from ferroelectric to the optical fields < Int. J.
Mech. Sci., 2020, 184 >, low regard was held in the biological field. The experimental design, synthetic methods or the microarchitecture-biological performance relationship of nanometamaterials for biological application have not been discussed. These results indicated that the nano-metamaterials, as a branch concept of metamaterials, have not gained strong attention and were mainly applied for physics applications. Therefore, an accessible design principle for 3D nano-metamaterials, which would further extend their application towards biology, is important for the development of nano-metamaterials and will provide inspirations for technicians and scientists to design novel classes of nano-metamaterials. On the basis of those considerations, we draw on a novel dual-kinetic controlled strategy to synthesize 3D nano-metamaterials, which comprised three parts: (i) the homogeneous interior core; (ii) an onion-like shell; and (iii) a hierarchically porous corona. We defined that nano-metamaterials were rationally designed materials with multilevel multiscale microarchitectures and both characteristic sizes and whole sizes at nanoscale, investing in themselves remarkably unique and significantly enhanced material properties, such as optical, ferroelectric and biological properties as compared with conventional nanoparticles. Compared to these previous reported works, our manuscript proposed a clear definition and novel synthesis protocol for the nanometamaterials with 3D microarchitecture. Furthermore, we extended the application of nanometamaterials to biological fields, manifesting a microarchitecture-biological performance relationship of nano-metamaterials. It should be noted that the remarkable properties were originated from the hierarchical complexity, as well as the intrinsic properties of the constituent chemicals. The suitable cosolvent (dichloromethane) of PEO-b-P2VP was found through theoretical analysis. The Flory-Huggins model is expressed interaction parameters for polymer-solvent and polymer-polymer segments at temperature T, which can be expressed as follows: where the χ − symbol represents polymer-solvent interaction parameter at absolute temperature T, represents molar volume of solvent, R is the gas constant, δ present solubility parameters of solvent and polymer (Table S2). [19] According to Flory Huggins theory standard, when χ − < 0.5, the polymer completely dissolved in the solvent among the whole composition range.